Monthly Archives: May 2025

Problem: Distinguish between the terms “intrinsic semiconductor” and “extrinsic semiconductor“. Solution: An intrinsic semiconductor is pretty much what it sounds like, i.e. a “pure” semiconductor material like \(\text{Si}\) that is undoped with any impurity dopants. An extrinsic semiconductor is then … Continue reading →

Problem: A vibrating string with displacement profile \(y(x,t)\) has non-uniform mass per unit length \(\mu(x)\) and non-uniform tension \(T(x)\) experiences both an internal restoring force due to \(T(x)\) but also a linear “Hooke’s law” restoring force \(-k(x)y(x)\) everywhere so that … Continue reading →

Problem: Why is it important to learn how to learn? Solution: In a post-AGI world where each day feels like swallowing a fire hose of new (mis!)information (especially as a researcher), the most important arrow one can have in the … Continue reading →

Problem: What is an estimator \(\hat{\theta}\) for some parameter \(\theta\) of a random variable? Distinguish between point estimators and interval estimators. Solution: In the broadest sense, an estimator is any function of \(N\) i.i.d. draws of the random variable \(\hat{\theta}(X_1,…,X_N)\). … Continue reading →

Problem: Explain what the spacetime complexity of an algorithm on a problem of characteristic input size \(n\) is. Solution: Time complexity \(T(n)\), is the number of \(\Theta(1)\)-operations that an algorithm requires to produce a solution to a problem of input … Continue reading →